The present invention relates to a method and apparatus for determining certain fluid flow parameters for naturally fractured media. In particular, a method and apparatus are provided whereby flow characteristics can be assessed at several fracture apertures within such media so that the impact of the fracture aperture on fluid flow may be accurately determined for reservoir modeling purposes.
In the production of oil, gas and other minerals, certain properties of the subterranean reservoir must be determined. Two of the key, most commonly measured properties are the porosity and permeability of the reservoir. The porosity of a material is the ratio of the aggregate volume of its void or pore spaces (i.e., pore volume) to its gross bulk volume and, in the case of an oil or gas reservoir, is a measure of the capacity within the reservoir rock which is available for storing oil or gas. The permeability of a material is a measure of the ability of the material to transmit fluids through its pore spaces and is inversely proportional to the flow resistance offered by the material. Additionally, fractures play an important role in reservoir behavior. Fractures have the ability to either enhance or restrict fluid flow in reservoirs and can alter the apparent permeability and/or porosity of the rock. Because of these important influences, the ability of fractures to conduct fluids must be fully understood in order to accurately model and effectively engineer a given reservoir.
Porosity and permeability are determined by taking core samples from the reservoir site and carrying out well-defined measurement techniques on the samples. There are several techniques available for making such measurements, many of which are described in Petroleum Production Engineering Development by L. C. Uren, Fourth Edition, McGraw-Hill Book Company, Inc., 1956, pps 660-669. Another standard reference for core sample analysis is the API Recommended Practice for Core-Analysis Procedure, API RP40, American Petroleum Institute, 1960, 55 pps. While these procedures are suitable for measuring the porosity and permeability of a sample, they do not address techniques capable of adequately assessing the contribution of reservoir fractures to overall production.
All reservoirs are probably fractured to some extent. Reservoir fracture systems are often complicated, interconnected arrays of fluid flow paths. However, flow in the simplest case, a single fracture, must be analyzed before an array can be studied. Flow in a single fracture has been traditionally characterized by the so-called Cubic law equation. This equation was developed for the case where steady-state isothermal, laminar flow between two parallel smooth plates exists.
Flow between parallel plates is an idealized case of single-phase flow and can not adequately represent all cases of flow in fractures. While the Cubic law relationship can represent laminar flow for viscous incompressible liquids in fractures of moderate size reasonably well, natural fractures behave quite differently from idealized, smooth surfaces when very narrow fractures are considered. Since the walls of natural rock fractures are not smooth and parallel, a method and apparatus useful in conducting tests to determine the impact of natural fractures on fluid flow is required.
Analogising the flow through fractures to the work conducted for pipe flow by L. F. Moody and reported in "Friction Factors for Pipe Flow", Transactions of ASME, 66, (1944), pps. 671-684, has been found to be useful. In Moody's work, a friction factor was developed for use in the calculation of pressure drop. The friction factor provides a measure of the resistance to flow caused by fluid drag on the surface and by internal mixing and is a dimensionless number. Another key factor, the Reynolds number, provides a dimensionless term representative of mass flow. The critical Reynolds number is that number at which flow changes from laminar to turbulent. Friction factors for turbulent flow are dependent upon the relative roughness of the pipe. In the turbulent flow regime, the rougher the pipe, the higher the friction factor. For laminar flow in pipes, the friction factor is not a function of surface roughness.
With regard to flow in fractures, friction factors can be used to account for the increase in pressure drop caused by fracture surface roughness. Through the use of pipe flow analogy, a modified Cubic law equation can be developed which avoids the smooth prallel plate assumption and is useful in the study of natural fracture phenomena. This equation will be correct for all single-phase, open fracture laminar and turbulent flow calculations, provided the correct friction factor is used. Friction factors may be developed experimentally using the method and apparatus of the present invention.
As stated by L. H. Reiss in "The Reservoir Engineering Aspects of Fractured Formations", Gulf Publishing Co., Houston, Tex., 1980, 108 pps., Darcy's law is relatable to fracture flow for the case of smooth parallel plate flow. Additionally, as was the case for the Cubic law, Darcy's law may also be modified to account for rough surfaces, as long as the correct friction factor is used.
Various past studies have experimently determined critical Reynolds numbers for viscous flow in fractured media. The range of reported results vary by a factor of four from the low to high value depending on the investigator. Surface roughness is believed responsible for this variance in findings, as well as the inherent instability of the transition zone between laminar and turbulent flow. For rough fractures, the critical Reynolds number decreases as fracture aperture decreases; that is, turbulent flow in small fractures will occur at lower velocities than previously expected. Normally, liquid flow in reservoirs is assumed to be laminar because of low fluid velocity; however, since fractures have high permeabilities, fluid velocities in reservoir fractures may reach the critical value in rough fractures.
As indicated, reservoir modeling of fractured reservoirs is clearly enhanced by accurate knowledge of the fracture surface roughness characteristics present in an oil field. Surface roughness may be accounted for in modeling by the friction fractor, itself a function of the Reynolds number flow parameter and the surface roughness to fracture aperture ratio (e/b), values all found to be highly reservoir fracture specific. While it is known in the art to manufacture fracture surfaces by gluing grains of sand to a smooth surface or by sawing a portion of a core sample in half, as done by Hurst in U.S. Pat. No. 3,162,037, reservoir modeling is enhanced through the use of natural fractures in flow characterization work.